Question

In Canadian football, after a touchdown the team has the opportunity to earn one more point by kicking the ball over the bar between the goal posts. The bar is 10.0 ft above the ground, and the ball is kicked from ground level, 36.0 ft horizontally from the bar in (Figure 1) . Football regulations are stated in English units, but convert to SI units for this problem.

A)There is a minimum angle above the ground such that if the ball is launched below this angle, it can never clear the bar, no matter how fast it is kicked. What is this angle? ===15.5
B) If the ball is kicked at 46.0 ∘ above the horizontal, what must its initial speed be if it is just to clear the bar? Express your answer in m/s.
I got part A but I can not figure out B

Answer 1

To find the initial speed required for the ball to just clear the bar, we can use the principles of projectile motion. By calculating the vertical displacement, initial vertical velocity, and time of flight, we can determine the necessary initial speed.

Step-by-step explanation:

To solve part B of the question, we need to use the principles of projectile motion. When a ball is kicked at an angle above the horizontal, we can break its initial velocity into horizontal and vertical components. The horizontal component remains constant throughout the motion, while the vertical component changes due to the acceleration due to gravity. In order to clear the bar, the ball needs to reach a certain vertical height. We can use the kinematic equation for vertical motion, which is d = v0yt - (1/2)gt2, where d represents the vertical displacement, v0y represents the initial vertical velocity, g represents the acceleration due to gravity, and t represents the time of flight.

Since the ball needs to reach a height of 10.0 ft, which is equivalent to 3.048 m, we can set d equal to this value. The initial vertical velocity is calculated using v0y = v0sin(theta), where v0 represents the initial speed and theta represents the launch angle above the horizontal. The time of flight can be calculated using t = 2v0y/g, where g is the acceleration due to gravity. Substituting these values into the kinematic equation and solving for v0, we can find the initial speed required for the ball to just clear the bar.